High Dimensional Bayesian Optimisation and Bandits via Additive Models

TL;DR

This paper introduces a scalable Bayesian Optimization method for high-dimensional functions with additive structure, demonstrating theoretical regret bounds and superior performance on various complex tasks.

Contribution

It proposes a new approach assuming additive functions, providing theoretical regret guarantees and improved empirical results over naive methods.

Findings

Regret depends linearly on dimension D for additive functions

Method outperforms naive Bayesian Optimization in experiments

Framework offers statistical and computational advantages

Abstract

Bayesian Optimisation (BO) is a technique used in optimising a $D$-dimensional function which is typically expensive to evaluate. While there have been many successes for BO in low dimensions, scaling it to high dimensions has been notoriously difficult. Existing literature on the topic are under very restrictive settings. In this paper, we identify two key challenges in this endeavour. We tackle these challenges by assuming an additive structure for the function. This setting is substantially more expressive and contains a richer class of functions than previous work. We prove that, for additive functions the regret has only linear dependence on $D$ even though the function depends on all $D$ dimensions. We also demonstrate several other statistical and computational benefits in our framework. Via synthetic examples, a scientific simulation and a face detection problem we demonstrate that our method outperforms naive BO on additive functions and on several examples where the function is not additive.